Question

story problem21

Answer 1

Look at both the garden and the area of the path as 2 rectangles. We know that the difference between the area of both rectangles is 360 ft².

So let's start with the area of the garden:
A= LxW -> A= 22ft x 15ft = 330ft²
the difference between the 2 rectangles is 360 ft²
We know that the garden+path area is 330ft² + 360ft² = 690ft²

now we're going to find the dimensions of the garden+path area:
Let's say x is the width of the path
Length of the big rectangle = 22 +2x
Width of the big rectangle = 15 +2x
(you add the x twice, because you want a path on all sides of the garden)

We also know that the area of the big rectangle is 690 ft² = (Length x Width)
So fill in the length and width that we found and that has to equal 690:
(2x+22)(2x+15)=690

And now we just have to find x:
4x² + 44x + 30x + 330 = 690 (use FOIL)
4x² + 44x + 30x + 330 -690 = 0 (subtract 690 from both sides)
4x² + 74x -360 = 0 (collect like terms)

Then use the quadratic formula:
\[x= (-b \pm \sqrt{b² -4ac} )/ 2a\]
\[x= (-74 \pm \sqrt{74² - 4.4.(-360)})/2.4\]
\[x= (-74 \pm106)/8\]

and we only need the positive solution:

\[x= (-74+106)/8\]
\[x=4\]